Singular limits of quasi-linear hyperbolic systems in a bounded domain of R3 with applications to Maxwell’s equations

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We establish a singular perturbation result for quasi-linear hyperbolic systems in a bounded domain of R3, depending on a small parameter. We prove and estimate the rate of convergence, as the parameter tends to zero, of uniformly stable solutions of the complete system to a solution of the reduced system. This result is then applied to the study of the convergence of the complete Maxwell equations to the quasi-stationary ones.

Original languageEnglish
Pages (from-to)111-129
Number of pages19
JournalPacific Journal of Mathematics
Volume116
Issue number1
DOIs
Publication statusPublished - Jan 1 1985

Fingerprint

Quasilinear Hyperbolic System
Singular Limit
Maxwell's equations
Bounded Domain
Stable Solution
Singular Perturbation
Small Parameter
Rate of Convergence
Tend
Zero
Estimate

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{bc43e6d990874aafb7ef798dc9c97f12,
title = "Singular limits of quasi-linear hyperbolic systems in a bounded domain of R3 with applications to Maxwell’s equations",
abstract = "We establish a singular perturbation result for quasi-linear hyperbolic systems in a bounded domain of R3, depending on a small parameter. We prove and estimate the rate of convergence, as the parameter tends to zero, of uniformly stable solutions of the complete system to a solution of the reduced system. This result is then applied to the study of the convergence of the complete Maxwell equations to the quasi-stationary ones.",
author = "Albert Milani",
year = "1985",
month = "1",
day = "1",
doi = "10.2140/pjm.1985.116.111",
language = "English",
volume = "116",
pages = "111--129",
journal = "Pacific Journal of Mathematics",
issn = "0030-8730",
publisher = "University of California, Berkeley",
number = "1",

}

TY - JOUR

T1 - Singular limits of quasi-linear hyperbolic systems in a bounded domain of R3 with applications to Maxwell’s equations

AU - Milani, Albert

PY - 1985/1/1

Y1 - 1985/1/1

N2 - We establish a singular perturbation result for quasi-linear hyperbolic systems in a bounded domain of R3, depending on a small parameter. We prove and estimate the rate of convergence, as the parameter tends to zero, of uniformly stable solutions of the complete system to a solution of the reduced system. This result is then applied to the study of the convergence of the complete Maxwell equations to the quasi-stationary ones.

AB - We establish a singular perturbation result for quasi-linear hyperbolic systems in a bounded domain of R3, depending on a small parameter. We prove and estimate the rate of convergence, as the parameter tends to zero, of uniformly stable solutions of the complete system to a solution of the reduced system. This result is then applied to the study of the convergence of the complete Maxwell equations to the quasi-stationary ones.

UR - http://www.scopus.com/inward/record.url?scp=84972569424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972569424&partnerID=8YFLogxK

U2 - 10.2140/pjm.1985.116.111

DO - 10.2140/pjm.1985.116.111

M3 - Article

AN - SCOPUS:84972569424

VL - 116

SP - 111

EP - 129

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -